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In the Quest for Invariant Structures Through Graph Theory, Groups and Mechanics: Methodological Aspects in the History of Applied Mathematics

  • Sandra VisokolskisEmail author
  • Carla Trillini
Conference paper
  • 39 Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11974)

Abstract

The purpose of this paper is to analyze a geometrical case study as a sample of an intended methodology based on invariant theory’s strategies, which have been developed particularly throughout the nineteenth century as one of the cornerstones of mathematics [15, p. 41], and whose resolution was reached by means of a combination of different disciplines: graph theory, mechanics and group theory, among others.

This case study presents the “perfect squared rectangle problem”, that is an exhaustive classification of the dissection of a rectangle into a finite number of unequal squares. Despite its simplicity, in both description and mathematical resolution, it provides plausible elements of generalization from “the ‘applied field’ of mathematics” [8, p. 658], as a special case of applied mathematical toolkit [1, p. 715], related to the practice of invariant strategies that remain fixed through changes.

Keywords

Invariants Graph theory Geometry 

Notes

Acknowledgements

This research was supported by the Research Group of Creativity and Innovation in Mathematics, National University of Villa Maria, Argentina.

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Authors and Affiliations

  1. 1.National University of CordobaCordobaArgentina
  2. 2.National University of Villa MariaCordobaArgentina

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